Gaussian boson sampling (GBS) is a computational process that can show quantum advantage under conservative assumptions [1]. This is because the output distribution of a network, consisting of squeezing and beamsplitter operations, can be mapped to a classically intractable operation on a matrix. Notable applications of GBS include the sampling of molecular spectra and the search of maximum cliques in graphs. Experimental realizations of GBS have been carried out both in photonics platforms [2] and cQED systems [3]. However, the former are limited by non-tunable squeezing strengths and challenging Fock state preparation. In the latter case, each bosonic mode is hosted by a bulky microwave cavity, which hinders the scaling beyond a few modes.
In contrast, high-overtone bulk acoustic resonators (HBARs) host a large density of long-lived phonon modes that can be well controlled in a circuit quantum acustodynamics (cQAD) device. I will present our work on implementing the building blocks of GBS based on bilinear interactions between HBAR modes coupled to a transmon qubit. In particular, we show how beamsplitter and squeezing operations can be realized by driving the ancilla qubit bichromatically. Using this parametric driving, we achieve up to 3dB of squeezing below the zero-point fluctuations and beamsplitter rates exceeding 20 kHz [4,5], allowing for gate times that are significantly shorter than the phonon coherence times of several hundred microseconds. Together with displacements and measurements of the Fock basis, these complete the universal continuous-variable gate set required for GBS. We show preliminary results on concatenating such gates as a step toward scalable GBS in cQAD.

[1] Hamilton, Craig S., et al. “Gaussian boson sampling.” Physical review letters 119.17 (2017): 170501.
[2] Arrazola, Juan M., et al. “Quantum circuits with many photons on a programmable nanophotonic chip.” Nature 591.7848 (2021): 54-60.
[3] Wang, Christopher S., et al. “Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor.” Physical Review X 10.2 (2020): 021060.
[4] Marti, Stefano, et al. “Quantum squeezing in a nonlinear mechanical oscillator.” Nature Physics 20.9 (2024): 1448-1453.
[5] von Lüpke, Uwe, et al. “Engineering multimode interactions in circuit quantum acoustodynamics.” Nature Physics 20.4 (2024): 564-570.